×

Improved particle swarm optimization combined with chaos. (English) Zbl 1074.90564

Summary: As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality.

MSC:

90C59 Approximation methods and heuristics in mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Phys Rev Lett, 64, 1196-1199 (1990) · Zbl 0964.37501
[2] Kapitaniak, T., Continuous control and synchronization in chaotic systems, Chaos, Solitons & Fractals, 6, 237-244 (1995) · Zbl 0976.93504
[3] Pecora, L.; Carroll, T., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[4] Aihara, K.; Takabe, T.; Toyoda, M., Chaotic neural networks, Phys Lett A, 144, 333-340 (1990)
[5] Li, B.; Jiang, W. S., Optimizing complex functions by chaos search, Cybernet Syst, 29, 409-419 (1998) · Zbl 1012.90068
[6] Lu, Z.; Shieh, L. S.; Chen, G. R., On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization, Chaos, Solitons & Fractals, 18, 819-827 (2003) · Zbl 1068.93053
[7] Wang, L.; Zheng, D. Z.; Lin, Q. S., Survey on chaotic optimization methods, Comput Technol Automat, 20, 1-5 (2001)
[8] Kennedy J, Eberhart RC. Particle swarm optimization. In: Proc IEEE Int Conf on Neural Networks, 1995, WA Australia. p. 1942-8; Kennedy J, Eberhart RC. Particle swarm optimization. In: Proc IEEE Int Conf on Neural Networks, 1995, WA Australia. p. 1942-8
[9] Kennedy, J.; Eberhart, R. C.; Shi, Y., Swarm intelligence (2001), Morgan Kaufmann Publishers: Morgan Kaufmann Publishers San Francisco
[10] Goldberg, D. E., Genetic algorithms in search, optimization, and machine learning (1989), Addison Wesley: Addison Wesley MA · Zbl 0721.68056
[11] Eberhart RC, Shi Y. Particle swarm optimization: developments, applications and resources. In: Proc. Congress on evolutionary computation, 2001, Seoul, Korea. p. 81-6; Eberhart RC, Shi Y. Particle swarm optimization: developments, applications and resources. In: Proc. Congress on evolutionary computation, 2001, Seoul, Korea. p. 81-6
[12] Angeline, P. J., Evolutionary optimization versus particle swarm optimization: philosophy and performance differences, (Evolutionary programming VII (1998), Springer), 601-610
[13] Shi, Y.; Eberhart, R. C., A modified particle swarm optimizer, (Proc IEEE Int Conf on Evolutionary Computation (1998), Anchorage: Anchorage USA), 69-73
[14] Shi Y, Eberhart RC. Empirical study of particle swarm optimization. In: Proc IEEE Int Congr Evolutionary Computation, 1999, Washington, DC. p. 1945-50; Shi Y, Eberhart RC. Empirical study of particle swarm optimization. In: Proc IEEE Int Congr Evolutionary Computation, 1999, Washington, DC. p. 1945-50
[15] May, R., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467 (1976) · Zbl 1369.37088
[16] Wang, L., Intelligent optimization algorithms with applications (2001), Tsinghua University & Springer Press: Tsinghua University & Springer Press Beijing
[17] Anderssen, R. S.; Jennings, L. S.; Ryan, D. M., Optimization (1972), University of Queensland Press: University of Queensland Press St. Lucia, Australia · Zbl 0305.00007
[18] Dekkers, A.; Aarts, E., Global optimizations and simulated annealing, Math Program, 50, 367-393 (1991) · Zbl 0753.90060
[19] Cvijović, D.; Klinowski, J., Taboo search: an approach to the multiple-minima problem, Science, 267, 664-666 (1995) · Zbl 1226.90101
[20] Ji, M. J.; Tang, H. W., Application of chaos in simulated annealing, Chaos, Solitons & Fractals, 21, 933-941 (2004) · Zbl 1045.37054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.